Analysis of an object data set on a multi-dimensional space

ABSTRACT

The method relates to analysis of a tubular structure  1  such as a rendition of the vascular system of a patient. Gradients g 1j  to the surface of the tubular structure  1  are computed in a starting point (BP). Subsequently, a normal {circumflex over (n)} which extends essentially perpendicularly to the gradients is derived and a cross-section is taken along a cutting plane having {circumflex over (n)} as its normal. A subsequent position (VP) is taken by performing a small shift in the direction of {circumflex over (n)}. The axis of the vessel is tracked by repeating the procedure.

The invention relates to a method of analyzing an object data set on amulti-dimensional space.

Such an object data set represents one or more properties of the objectto be examined. The object data set notably relates to the densitydistribution in the object to be examined; in that case the data valuesare the local density values of (a part of) the object to be examined.The data values may also relate, for example, to the distribution of thetemperature or the magnetization in the object. The multi-dimensionalspace is usually the three-dimensional space. The data values thenrelate to a volume distribution of the relevant property, for example,the density distribution in a volume of the object to be examined. Themulti-dimensional space may also be two-dimensional. In that case thedata values relate to a distribution of the relevant property in a planethrough the object, for example the density distribution in across-section through the object.

The object data set can be acquired in a variety of ways. The objectdata set notably relates to a patient to be examined. Such an objectdata set can be acquired by means of various techniques such as 3D X-rayrotational angiography, computed tomography, magnetic resonance imagingor magnetic resonance angiography.

The article “3D rotational angiography: Clinical value in endovasculartreatment” in Medica Mundi 42 (1998) by J. Moret et al. concerns thedetermination of the section of a blood vessel.

According to the known method a more or less tubular structure relatingto the blood vessel of the patient to be examined is identified from theobject data set. Such an identification is performed on the basis ofdifferences between data values relating to the blood vessel and to thesurrounding tissue. Such differences are realized by introducing asuitable contrast agent into the vascular system of the patient to beexamined during the acquisition of the object data set. According to theknown method a cutting plane is visually taken in the object data set soas to extend more or less transversely of the tubular structure.Subsequently, the diameter of the relevant blood vessel is calculatedfrom the cross-section of the tubular structure along the cutting plane.

It is a drawback of the known method that it is difficult to orient thecutting plane so as to extend accurately perpendicularly to the tubularstructure. This inaccuracy introduces serious errors in the calculateddiameter of the relevant blood vessel.

It is an object of the invention to provide a method wherein analysis ofa tubular structure in the object data offers more accurate results thanthe known method. It is notably an object of the invention to provide amethod whereby the diameter of such a tubular structure can beaccurately determined.

This object is achieved according to the invention by means of a methodof analyzing an object data set in which a tubular structure occurs,wherein

-   -   said object data set assigns data values to positions in a        multi-dimensional space, which data values relate to an object        to be examined,    -   a starting position is chosen in or near the tubular structure,    -   gradients to the surface of the tubular structure are derived at        the area of the starting position,    -   a cutting plane is derived through the starting position so as        to have a direction as parallel as possible to the gradients in        positions to the surface of the tubular structure and in a        vicinity of the starting position, and    -   a cross-section of the tubular structure is derived along the        cutting plane.

The object data set can be acquired, for example, by means of varioustechniques such as magnetic resonance angiography, computed tomographyor 3D rotational X-ray angiography. Techniques of this kind produce anobject data set with data values representing the structure of (a partof) the vascular system of the patient to be examined.

The tubular structure concerns a part of the object data set in whichthe data values deviate from the surroundings of the tubular structure.The deviating data values lie, for example, in a selected range of datavalues which are larger than a predetermined threshold or smaller than apredetermined ceiling value. The positions in the multi-dimensionalspace for which the data values have such a deviating value are situatedin an elongate, more or less tubular region. This tubular region may beshaped as a vacated or a filled tube. The tubular structure can beindicated in the object data set by means of segmentation techniques,thus identifying the positions with the deviating data values.

The starting position indicates the position in which the cross-sectionof the tubular structure is desired. The starting position can beindicated, for example, by pointing it out in a rendition of the objectdata set on a display screen.

The gradients concern local differences between data values at the areaof the surface. According to the invention the normal vector to thecutting plane is oriented exactly transversely of the gradients to thesurface. The normal vector is oriented in such a manner that the normalvector is perpendicular to the gradients with a small tolerance only.The cutting plane can thus be oriented substantially parallel to thetubular structure. As a result, the diameter of the tubular structurecan be accurately derived from the cross-section of the tubularstructure. This diameter represents, for example, a useful technicalresult of the examination of the vascular system of the patient to beexamined. It is notably possible to perform an accurate examination ofstenoses or aneurysms.

These and other aspects of the invention will be described in detailhereinafter on the basis of the following embodiments which are definedin the dependent claims.

The normal vector to the cutting plane is oriented, for example, byminimizing the weighted sum of the squares of the scalar products of thenormal vector and the gradients to the surface of the tubular structurein a (small) vicinity of the starting position while varying the normalvector to the cutting plane. The weights in the weighted sum can beused, for example to make the effect of gradients in positions nearer tothe starting point on the normal vector to the cutting plane greaterthan the effect of gradients in positions situated somewhat further fromthe starting position.

Preferably, a local center of the tubular structure in the cutting planeis derived from positions in the cutting plane having data values in theselected range. This local center represents the center of the tubularstructure in the cross-section along the cutting plane. For example, thelocal center is situated in a position which is situated atapproximately the same distance from practically all positions in thecutting plane having data values in the selected range. It has beenfound that in many cases the vast majority of such positions having datavalues in the selected range and in the cutting plane representlocations at the edge of the tubular structure. Preferably, positions inwhich the gradients have a magnitude greater than a minimum value areused to derive the local center. Positions at the edge of the tubularstructure are thus accurately selected.

An even more accurate result for the local center is achievediteratively by means of the method defined in claim 4. Preferably, asubdivision into four equally large sectors is used. Positions outsidethe relevant tubular structure are excluded by determining the minimumdistance of positions having data values in the selected range in eachsector. When different minimum distances from the current centerposition of the local center occur in different sectors, the currentcenter position will not be situated exactly at the center of thetubular structure. A more accurate estimate of the center position isobtained by shifting the center position slightly in the direction ofthe sector in which the largest minimum distance occurs. Preferably, thecenter position is shifted over a distance corresponding to half thedifference between the minimum distances in oppositely situated sectors.

According to the invention it is also possible to track the longitudinalaxis of the tubular structure. To this end there is derived a subsequentposition which is shifted in the direction of the normal to the cuttingplane in the starting position. A next cutting plane through thesubsequent position is then derived in conformity with claim 1. In thenext cutting plane a local center of the cross-section through thetubular structure is determined again. Successive local centers arederived along the tubular structure by repetition. The magnitude of theshift along the tubular structure can be chosen by the user. Thetracking of the tubular structure will be more exact as the shifts forderiving each time a next subsequent position are smaller. Preferably, aseries of diameters is calculated for the series of cross-sectionsthrough the tubular structure thus obtained along respective cuttingplanes. This offers a thorough insight into the variation of thediameter of the tubular structure along the longitudinal axis of thestructure. This result constitutes a useful aid for examining the extentof stenosis in the vascular system of the patient to be examined.

The invention is preferably used for tracking a tubular structure whichincludes a reservoir whereto inlet and outlet ducts are connected. Thereservoir typically has a diameter which is significantly larger thanthat of the inlet and outlet ducts. Such a situation occurs, forexample, in the case of an aneurysm. The actual aneurysm thencorresponds to the reservoir whereas the inlet and outlet ductscorrespond to the blood vessels feeding and draining the blood to andfrom the actual aneurysm. The method disclosed in claim 6 is preferablyused in such a situation. According to the invention the inlet andoutlet points can be determined by tracking the inlet and outlet ductsin conformity with claim 5. Preferably, such tracking of the inlet andoutlet ducts is observed on a monitor by the user who can terminate thetracking operation as soon as the connections to the reservoir arereached. Subsequently, a central position is determined in thereservoir. For example, a part of the object data set which contains thereservoir and a small (relative to the reservoir) number of positionsoutside the reservoir is selected. It has been found that the center ofgravity of the data values in the selected part of the object data setsuitably corresponds to the center of the reservoir. The cutting planethrough the inlet and outlet points and through the center of thereservoir separates the reservoir from the inlet and outlet ducts. Thevolume of the reservoir to the side of the cutting surface which facesthe central position accurately represents the effective volume of thereservoir. When the reservoir with the inlet and outlet ducts representsan aneurysm and the connected blood vessels, the effective volume of thereservoir constitutes an accurate result concerning the size of theaneurysm; this is of importance for the further treatment of theaneurysm.

Preferably, the method is carried out by means of a suitably programmedworkstation. For example, a computer program with instructions forcarrying out the steps as defined in the claims 1 to 7 is loaded intosuch a workstation.

Claim 7 defines a further application of the invention for a tubularstructure with a reservoir whereto inlet and outlet ducts are connected.The inlet and outlet points are determined again by tracking the inletand outlet ducts in conformity with claim 5. According to thisapplication of the invention a connection duct is interpolated betweenthe inlet point and the outlet point and through the reservoir.Subsequently, the connection duct is isolated from the reservoir. It hasbeen found that the remainder constitutes a good approximation of theeffective reservoir which can be suitably used for determining the sizeof the aneurysm.

These and other aspects of the invention will be elucidated, by way ofnon-limitative example, with reference to the following embodiments andthe accompanying drawing; therein:

FIG. 1 shows an example of an object data set with a tubular structurein which the application of the invention is indicated, and

FIG. 2 shows an example of a flow chart of the method according to theinvention.

FIG. 1 shows an example of an object data set containing a tubularstructure in which the application of the invention is indicated. FIG. 2shows an example of a flow chart of the method according to theinvention. FIG. 1 notably shows the tubular structure, in this case arendition of a part of the vascular system of the patient to beexamined, which has already been segmented from the possibly largerobject data set. This is represented by the step 10 in FIG. 2. Thesegmentation consists, for example, in that all data values are set to afixed value in positions in which the original object data set containsdata values outside the selected range. The vascular system includes ananeurysm 3 which acts as a reservoir, a blood vessel 2 which transportsblood to the aneurysm 3 and a blood vessel 4 via which blood isdischarged from the aneurysm 3. The blood vessels 2 and 4 thus act as aninlet duct and an outlet duct. The starting point (BP) is selected bythe user, for example by pointing it out on the display screen of aworkstation by means of a mouse and/or a keyboard and a cursor. Aroundthe starting point (BP) there is taken a sphere (B1) as indicated instep 20. The gradients (g_(1j)) of the data values are calculated atpoints on the edge of the tubular structure in the sphere (B1); this isindicated in step 30. More explicitly the gradients are calculated asfollows: ${g_{1_{j}} = \begin{pmatrix}\frac{\partial D}{\partial x_{j}} \\\frac{\partial D}{\partial y_{j}} \\\frac{\partial D}{\partial z_{j}}\end{pmatrix}},$where (x_(j),y_(j),z_(j)) is the position at issue at the surface of thetubular structure and D indicates the data-values of the data-set whichrepresent for example the pixel-values or the voxel-values of the objectto be examined. Consequently, the vector g_(1j) points transverse to thesurface of the tubular structure. Subsequently, in step 40 the normalvector {circumflex over (n)}₁ is calculated by means of a minimizationprocess, so that the sum Σ_(j)w_(j)({circumflex over (n)}₁·g_(1j))² isminimum. The weight factors w_(j) are to be adjusted by the user;preferably, the weight factors decrease as the distance between theposition in which the gradient g_(1j) is calculated and the startingpoint BP is larger. The cutting plane SN1 has a normal vector{circumflex over (n)}₁ and extends through the starting point BP. Thecross-section through the tubular structure 1 along the cutting planeSN1 is taken in step 50. In step 51 the local diameter d of the tubularstructure 1, i.e. of the blood vessel, is derived from thiscross-section. Furthermore, in step 52 the local center position of thetubular structure is derived from the cross-section by executing theiterative procedure in conformity with claim 4.

In order to track the tubular structure as from the starting point BP,in step 60 the subsequent position VP is derived in the direction of thenormal vector {circumflex over (n)}₁ which is locally orientedaccurately along the axis of the blood vessel. The magnitude of theshift is adjusted by the user in dependence on the degree of meanderingof the tubular structure. FIG. 1 shows a subsequent position VP which isreached after a large number of shifts along the axis of the bloodvessel 2. When the subsequent position is not yet the end position (EP)desired by the user, the steps 20, 30, 40, 50, 51, 52 and 60 arerepeated. Thus, the axis along the blood vessel and the diameter alongthe axis are thus determined.

For example, the end point EP is the inlet point TP from the bloodvessel 2 to the aneurysm 3. The outlet point AP is reached by trackingthe blood vessel from a different starting point BP′ on the blood vessel4 by means of the procedure shown in FIG. 2. For example, the userhimself can terminate the tracking of the blood vessel when, on thebasis of the anatomical insight of the user, the inlet point or outletpoint has been reached. It is also possible to terminate the tracking ofthe blood vessel when the local diameter of the blood vessel suddenlyincreases strongly. A connecting line 1 is drawn through the inlet pointand the outlet point (TP, AP). Furthermore, the central position Z ofthe aneurysm 3 is calculated as the center of gravity on the basis ofthe data values in the region G. The region G is, for example, a spherearound the aneurysm 3. It has been found that suitable results areachieved for the center position Z when it is ensured that the region Gdoes not include too many points in the segmented data set which lieoutside the aneurysm. The normal vector {circumflex over (m)} isdirected opposite to the perpendicular from Z to the connecting line 1.Subsequently, a cutting plane SN3 is determined through the connectingline and with the normal vector {circumflex over (m)}. It appears thatthis cutting plane SN3 accurately separates the inlet and outlet ducts,in this case being the blood vessels 2 and 4, from the aneurysm 3.

1. A computer-implemented method of analyzing an object data set inwhich a tubular structure occurs, wherein said object data set assignsdata values to positions in a multi-dimensional space, which data valuesrelate to an object to be examined, a starting position is chosen in ornear the tubular structure, gradients to the surface of the tubularstructure are derived at the area of the starting position, a cuttingplane is derived through the starting position so as to have a directionas parallel as possible to the gradients in positions to the surface ofthe tubular structure and in a vicinity of the starting position, and across-section of the tubular structure is derived along the cuttingplane.
 2. A method as claimed in claim 1, wherein the direction of thecutting plane is derived by minimization of the sum of the squares ofthe scalar products of the normal vector to the cutting plane and thegradients.
 3. A method as claimed in claim 1, wherein a local center ofthe tubular structure in the cutting plane is derived from positions inthe cutting plane having data values within a predetermined range, sucha range concerning notably data values higher than a threshold value ordata values smaller than a ceiling value.
 4. A method as claimed inclaim 3, wherein the cutting plane is subdivided into a plurality ofsectors and a center position of the local center of the cross-sectionof the tubular structure in the cutting plane is estimated, for therespective sectors a minimum distance is derived between positionshaving data values in the preselected range and a current estimatedcenter position, a maximum of the minimum distances in the respectivesectors is determined, a new estimate of the center position is derived,the new estimate of the center position being shifted, relative to thecurrent estimate, in the cutting plane in the direction of the sector inwhich the maximum of the minimum distances is situated and over adistance which is dependent on the differences between positions inwhich the minimum distances occur in oppositely situated sectors, thesteps b, c and d are repeated, if necessary, the new estimate of thecenter position being used each time as the current estimate.
 5. Amethod as claimed in claim 3, wherein a subsequent position which hasbeen shifted, relative to the starting position, in the direction of thenormal to the cutting plane through the starting position is determined,and a subsequent cutting plane through the subsequent position isderived, the direction of said subsequent cutting plane being asparallel as possible to the gradients in said subsequent cutting planeand to the surface of the tubular structure.
 6. A computer-implementedmethod of analyzing an object data set in which a tubular structureoccurs, wherein said object data set adds data values to positions in amulti-dimensional space, an inlet duct, an outlet duct and a reservoiroccur in the tubular structure, the inlet and outlet ducts beingconnected to the reservoir, and an inlet point is determined in theinlet duct at the area of connection of the inlet duct to the reservoir,an outlet point is determined in the outlet duct at the area ofconnection of the outlet duct to the reservoir, a central position ofthe reservoir is determined, and a cutting plane through the inlet andoutlet points is derived, the normal to the cutting plane extendingalong the perpendicular from the central position to the line throughthe inlet and outlet points.
 7. A computer-implemented method ofanalyzing an object data set in which a tubular structure occurs,wherein said object data set adds data values to positions in amulti-dimensional space, an inlet duct, an outlet duct and a reservoiroccur in the tubular structure, the inlet and outlet ducts beingconnected to the reservoir, and an inlet point is determined in theinlet duct at the area of connection of the inlet duct to the reservoir,an outlet point is determined in the outlet duct at the area ofconnection of the outlet duct to the reservoir, a connecting duct isinterpolated between the inlet and outlet points and through thereservoir, and a remainder is derived as the difference between thereservoir and the interpolated connecting duct.
 8. A computer programmeembodied on a tangible medium for analysing an object data set in whicha tubular structure occurs, the object data set assigning data values topositions in a multi-dimensional space, which data values relate to anobject to be examined, the computer programme comprising instructionsfor choosing starting position in or near the tubular structure derivinggradients to the surface of the tubular structure are derived at thearea of the starting position deriving a cutting plane through thestarting position so as to have a direction as parallel as possible tothe gradients to the surface of the tubular structure in positions inthe vicinity of the starting position and deriving a cross section ofthe tubular structure along the cutting plane.